Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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\left(\frac{7}{12}+\frac{245}{50}\times \frac{x}{48+52}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Reduce the fraction \frac{28}{48} to lowest terms by extracting and canceling out 4.
\left(\frac{7}{12}+\frac{49}{10}\times \frac{x}{48+52}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Reduce the fraction \frac{245}{50} to lowest terms by extracting and canceling out 5.
\left(\frac{7}{12}+\frac{49}{10}\times \frac{x}{100}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Add 48 and 52 to get 100.
\left(\frac{7}{12}+\frac{49x}{10\times 100}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Multiply \frac{49}{10} times \frac{x}{100} by multiplying numerator times numerator and denominator times denominator.
\left(\frac{7\times 250}{3000}+\frac{3\times 49x}{3000}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 10\times 100 is 3000. Multiply \frac{7}{12} times \frac{250}{250}. Multiply \frac{49x}{10\times 100} times \frac{3}{3}.
\frac{7\times 250+3\times 49x}{3000}\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Since \frac{7\times 250}{3000} and \frac{3\times 49x}{3000} have the same denominator, add them by adding their numerators.
\frac{1750+147x}{3000}\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Do the multiplications in 7\times 250+3\times 49x.
\frac{1750+147x}{3000}\times 0+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Multiply 0 and 1 to get 0.
0+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Anything times zero gives zero.
0+\frac{4}{5}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.
0+0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Multiply \frac{4}{5} and 0 to get 0.
0+0+\frac{15}{30}\times 0\times 75=0\times 5
Multiply 0 and 15 to get 0.
\frac{15}{30}\times 0\times 75=0\times 5
Add 0 and 0 to get 0.
\frac{1}{2}\times 0\times 75=0\times 5
Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.
0\times 75=0\times 5
Multiply \frac{1}{2} and 0 to get 0.
0=0\times 5
Multiply 0 and 75 to get 0.
0=0
Multiply 0 and 5 to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{C}
This is true for any x.
\left(\frac{7}{12}+\frac{245}{50}\times \frac{x}{48+52}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Reduce the fraction \frac{28}{48} to lowest terms by extracting and canceling out 4.
\left(\frac{7}{12}+\frac{49}{10}\times \frac{x}{48+52}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Reduce the fraction \frac{245}{50} to lowest terms by extracting and canceling out 5.
\left(\frac{7}{12}+\frac{49}{10}\times \frac{x}{100}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Add 48 and 52 to get 100.
\left(\frac{7}{12}+\frac{49x}{10\times 100}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Multiply \frac{49}{10} times \frac{x}{100} by multiplying numerator times numerator and denominator times denominator.
\left(\frac{7\times 250}{3000}+\frac{3\times 49x}{3000}\right)\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 10\times 100 is 3000. Multiply \frac{7}{12} times \frac{250}{250}. Multiply \frac{49x}{10\times 100} times \frac{3}{3}.
\frac{7\times 250+3\times 49x}{3000}\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Since \frac{7\times 250}{3000} and \frac{3\times 49x}{3000} have the same denominator, add them by adding their numerators.
\frac{1750+147x}{3000}\times 0\times 1+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Do the multiplications in 7\times 250+3\times 49x.
\frac{1750+147x}{3000}\times 0+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Multiply 0 and 1 to get 0.
0+\frac{8}{10}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Anything times zero gives zero.
0+\frac{4}{5}\times 0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.
0+0\times 15+\frac{15}{30}\times 0\times 75=0\times 5
Multiply \frac{4}{5} and 0 to get 0.
0+0+\frac{15}{30}\times 0\times 75=0\times 5
Multiply 0 and 15 to get 0.
\frac{15}{30}\times 0\times 75=0\times 5
Add 0 and 0 to get 0.
\frac{1}{2}\times 0\times 75=0\times 5
Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.
0\times 75=0\times 5
Multiply \frac{1}{2} and 0 to get 0.
0=0\times 5
Multiply 0 and 75 to get 0.
0=0
Multiply 0 and 5 to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{R}
This is true for any x.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}